Pricing by arbitrage

Unlike the CAPM, which assume markets are perfectly efficient, APT assumes markets sometimes misprice securities, before the market eventually corrects and securities move back to fair value.

Arbitrage pricing theory assumptions

The APT model does not require any assumption about the empirical distribution of the asset returns, unlike CAPM which assumes that stock returns follow a normal distribution and thus APT a less restrictive model. Most academics use three to five factors to model returns, but the factors selected have not been empirically robust. This relationship is a fundamental result with many applications to financial theory. It assumes that each investor will hold a unique portfolio with its own particular array of betas, as opposed to the identical "market portfolio". As a result, this issue is essentially empirical in nature. The macroeconomic factors that have proven most reliable as price predictors include unexpected changes in inflation, gross national product GNP , corporate bond spreads and shifts in the yield curve. The arbitrageur is thus in a position to make a risk-free profit: Where today's price is too low: The implication is that at the end of the period the portfolio would have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at more than this rate. Consequently, the linear pricing rule states that the price of this bond is equal to the price of a bundle of nine Arrow securities three of the type which pay in state 1, four of which pay in state 2, etc. In some ways, the CAPM can be considered a "special case" of the APT in that the securities market line represents a single-factor model of the asset price, where beta is exposed to changes in value of the market. A correctly priced asset here may be in fact a synthetic asset - a portfolio consisting of other correctly priced assets. A disadvantage of APT is that the selection and the number of factors to use in the model is ambiguous. Notice that the no-arbitrage condition, which guaranteed the existence of positive state prices m 1, m 2,..

Unlike the CAPM, the APT, however, does not itself reveal the identity of its priced factors - the number and nature of these factors is likely to change over time and between economies.

Finding and listing all factors can be a difficult task and runs a risk of some or the other factor being ignored.

However, this is not a risk-free operation in the classic sense of arbitragebecause investors are assuming that the model is correct and making directional trades—rather than locking in risk-free profits. Mechanics[ edit ] In the APT context, arbitrage consists of trading in two assets — with at least one being mispriced.

arbitrage pricing theory diagram

The question is how to interpret this last term. Thus, factor shocks would cause structural changes in assets' expected returns, or in the case of stocks, in firms' profitabilities.

arbitrage pricing theory cfa

Then i the return on any given asset f with payoffs can be expressed as a linear combination of returns on the n fundamental assets, i. So, the expected return is calculated taking into account various factors and their sensitivities that might affect the stock price movement.

Arbitrage pricing theory advantages and disadvantages

The question is how to interpret this last term. Using APT, arbitrageurs hope to take advantage of any deviations from fair market value. A disadvantage of APT is that the selection and the number of factors to use in the model is ambiguous. Arbitrage Pricing Theory Limitations The model requires a short listing of factors that impact the stock under consideration. However, an alternative to this is to assume that the factors are latent variables and employ factor analysis - akin to the form used in psychometrics - to extract them. Consequently, the linear pricing rule states that the price of this bond is equal to the price of a bundle of nine Arrow securities three of the type which pay in state 1, four of which pay in state 2, etc. Notice that to obtain the linear pricing rule, we required unlimited short-sales - a proposition which directly goes against Radner 's assumption of a lower bound to ensure existence of a Radner equilibrium. Moreover, the sensitivities associated may also undergo shifts which need to be continuously monitored making it very difficult to calculate and maintain. Unlike the CAPM, which assume markets are perfectly efficient, APT assumes markets sometimes misprice securities, before the market eventually corrects and securities move back to fair value. This portfolio has the same exposure to each of the macroeconomic factors as the mispriced asset. Also, the risk of accidental correlations may exist which may cause a factor to become substantial impact provider or vice versa. The macroeconomic factors that have proven most reliable as price predictors include unexpected changes in inflation, gross national product GNP , corporate bond spreads and shifts in the yield curve. At the end of the period: 1 sell the portfolio 2 use the proceeds to buy back the mispriced asset 3 pocket the difference. The arbitrageur is thus in a position to make a risk-free profit: Where today's price is too low: The implication is that at the end of the period the portfolio would have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at more than this rate.

Several a priori guidelines as to the characteristics required of potential factors are, however, suggested: their impact on asset prices manifests in their unexpected movements they should represent undiversifiable influences these are, clearly, more likely to be macroeconomic rather than firm-specific in nature timely and accurate information on these variables is required the relationship should be theoretically justifiable on economic grounds Chen, Roll and Ross identified the following macro-economic factors as significant in explaining security returns: surprises in GNP as indicated by an industrial production index; surprises in investor confidence due to changes in default premium in corporate bonds; surprise shifts in the yield curve.

In some ways, the CAPM can be considered a "special case" of the APT in that the securities market line represents a single-factor model of the asset price, where beta is exposed to changes in value of the market.

Thus, it allows the selection of factors that affect the stock price largely and specifically. Let us now look at some arbitrage pricing theory advantages and disadvantages summarized as under: Arbitrage Pricing Theory Benefits APT model is a multi-factor model.

Let us now define the financial return of asset f in state s, Rfs, as the value of the payoff divided by the purchasing price minus 1, i.

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Arbitrage pricing theory